Large Margin Graph Embedding-Based Discriminant Dimensionality Reduction

Discriminant graph embedding-based dimensionality reduction methods have attracted more and more attention over the past few decades. These methods construct an intrinsic graph and penalty graph to preserve the intrinsic geometry structures of intraclass samples and separate the interclass samples. However, the marginal samples cannot be accurately characterized only by penalty graphs since they treat every sample equally. In practice, these marginal samples often influence the classification performance, which needs to be specially tackled. In this study, the near neighbors’ hypothesis margin of marginal samples has been further maximized to separate the interclass samples and improve the discriminant ability by integrating intrinsic graph and penalty graph. A novel discriminant dimensionality reduction named LMGE-DDR has been proposed. Several experiments on public datasets have been conducted to verify the effectiveness of the proposed LMGE-DDR such as ORL, Yale, UMIST, FERET, CMIU-PIE09, and AR. LMGE-DDR performs better than other compared methods, and the corresponding standard deviation of LMGE-DDR is smaller than others. This demonstrates that the evaluation method verifies the effectiveness of the introduced method.

Pressure infiltration of molten aluminum for densification of environmental barrier coatings

Environmental barrier coatings (EBCs) effectively protect the ceramic matrix composites (CMCs) from harsh engine environments, especially steam and molten salts. However, open pores inevitably formed during the deposition process provide the transport channels for oxidants and corrosives, and lead to premature failure of EBCs. This research work proposed a method of pressure infiltration densification which blocked these open pores in the coatings. These results showed that it was difficult for aluminum to infiltrate spontaneously, but with the increase of external gas pressure and internal vacuum simultaneously, the molten aluminum obviously moved forward, and finally stopped infiltrating at a depth of a specific geometry. Based on the wrinkled zigzag pore model, a mathematical relationship between the critical pressure with the infiltration depth and the pore intrinsic geometry was established. The infiltration results confirmed this relationship, indicating that for a given coating, a dense thick film can be obtained by adjusting the internal and external gas pressures to drive a melt infiltration.

A functional skeleton transfer

The animation community has spent significant effort trying to ease rigging procedures. This is necessitated because the increasing availability of 3D data makes manual rigging infeasible. However, object animations involve understanding elaborate geometry and dynamics, and such knowledge is hard to infuse even with modern data-driven techniques. Automatic rigging methods do not provide adequate control and cannot generalize in the presence of unseen artifacts. As an alternative, one can design a system for one shape and then transfer it to other objects. In previous work, this has been implemented by solving the dense point-to-point correspondence problem. Such an approach requires a significant amount of supervision, often placing hundreds of landmarks by hand. This paper proposes a functional approach for skeleton transfer that uses limited information and does not require a complete match between the geometries. To do so, we suggest a novel representation for the skeleton properties, namely the functional regressor, which is compact and invariant to different discretizations and poses. We consider our functional regressor a new operator to adopt in intrinsic geometry pipelines for encoding the pose information, paving the way for several new applications. We numerically stress our method on a large set of different shapes and object classes, providing qualitative and numerical evaluations of precision and computational efficiency. Finally, we show a preliminar transfer of the complete rigging scheme, introducing a promising direction for future explorations.

Pressure Infiltration of Molten Aluminum for Densification of Environmental Barrier Coatings

Environmental barrier coatings (EBCs) effectively protect ceramic matrix composites (CMCs) from harsh engine environment, especially steam and molten salts. However, open pores inevitably formed during deposition process provide transport channels for oxidants and corrosives and lead to premature failure of EBCs. This work proposed a pressure infiltration densification method that blocked these open pores in the coatings. Results showed that it was difficult for aluminum to infiltrate spontaneously, but with the increase of external gas pressure and internal vacuum simultaneously, the molten aluminum obviously moved forward, but finally stopped infiltrating at a depth of a specific geometry. Based on the wrinkled zigzag pore model, a mathematical relationship between the critical pressure and the infiltration depth and the pore intrinsic geometry was established. Infiltration results confirmed this relationship, indicating that for a given coating, a dense thick film can be obtained by adjusting the internal and external gas pressures to drive the melt infiltration.

Coarse median algebras: the intrinsic geometry of coarse median spaces and their intervals

This paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra which simultaneously generalises the concepts of bounded geometry coarse median spaces and classical discrete median algebras. We study the coarse median universe from the perspective of intervals, with a particular focus on cardinality as a proxy for distance. In particular we prove that the metric on a quasi-geodesic coarse median space of bounded geometry can be constructed up to quasi-isometry using only the coarse median operator. Finally we develop a concept of rank for coarse median algebras in terms of the geometry of intervals and show that the notion of finite rank coarse median algebra provides a natural higher dimensional analogue of Gromov’s concept of $$\delta $$ δ -hyperbolicity.

Geometry of Nonholonomic Kenmotsu Manifolds

The concept of the intrinsic geometry of a nonholonomic Kenmotsu manifold M is introduced. It is understood as the set of those properties of the manifold that depend only on the framing of the D^ distribution D of the manifold M, on the parallel transformation of vectors belonging to the distribution D along curves tangent to this distribution. The invariants of the intrinsic geometry of the nonholonomic Kenmotsu manifold are: the Schouten curvature tensor; 1-form η generating the distribution D; the Lie derivative of the metric tensor g along the vector field ; Schouten — Wagner tensor field P, whose components in adapted coordinates are expressed using the equalities . It is proved that, as in the case of the Kenmotsu manifold, the Schouten — Wagner tensor of the manifold M vanishes. It follows that the Schouten tensor of a nonholonomic Kenmotsu manifold has the same formal properties as the Riemann curvature tensor. It is proved that the alternation of the Ricci — Schouten tensor coincides with the differential of the structural form. This property of the Ricci — Schouten tensor is used in the proof of the main result of the article: a nonholonomic Kenmotsu manifold cannot carry the structure of an η-Einstein manifold.